Concentric ring electrodes for improved accuracy of laplacian estimation

ABSTRACT

An electrode device for electrophysiological measurement may include an electrode substrate having a surface area. The electrode device may include a central electrode disposed on the electrode substrate around a central portion of the surface area. The electrode device may include a plurality of electrodes disposed on the electrode substrate concentric with the central electrode. The plurality of electrodes may include a first electrode covering a first portion of the surface area of the electrode substrate and a second electrode covering a second portion of the surface area of the electrode substrate. The second portion may be greater than a combined surface area of the first portion and the central portion.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.17/067,480, filed Oct. 9, 2020, which is incorporated by referenceherein in its entirety.

STATEMENT AS TO FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT

Embodiments of the present disclosure were developed with governmentsupport under award numbers 1622481 and 1914787 to Oleksandr Makeyev,awarded by the National Science Foundation (NSF) Division of HumanResource Development (HRD) Tribal Colleges and Universities Program(TCUP). The government has certain rights thereto.

BACKGROUND

Electroencephalography (EEG) is an essential tool for brain andbehavioral research, as well as one of the mainstays of hospitaldiagnostic procedures and pre-surgical planning. Despite EEG's manyadvantages, the technology faces challenges such as poor spatialresolution, selectivity and low signal-to-noise ratio.

Noninvasive concentric ring electrodes (CREs) can resolve many of theseproblems. Noninvasive CREs have been shown to estimate the surfaceLaplacian, the second spatial derivative of the potentials on the scalpsurface for the case of electroencephalogram, directly at each electrodeinstead of combining the data from an array of conventional, singlepole, disc electrodes. Compared to EEG via disc electrodes, EEG viatripolar CREs has been demonstrated to have significantly better spatialselectivity, signal-to-noise ratio, and mutual information. CREs havefound applications in a wide range of areas including brain-computerinterfaces, epileptic seizure onset detection, detection ofhigh-frequency oscillations, which may typically predict or precedeseizures, and seizure onset zones, as well as in applications involvingelectroenterograms, electrocardiograms, and electrohysterograms. CREscould also be used for electrophysiological monitoring, e.g., duringsurgery.

BRIEF SUMMARY

Electrode devices and methods for electrophysiological measurement areprovided. An electrode device may include an electrode substrate havinga surface area. The electrode device may include a central discelectrode disposed on the electrode substrate and covering a centralportion of the surface area. The central disc electrode may have a firstradius, “R,” of the central disc electrode relative to a center point ofthe central disc electrode. The electrode device may include a middlering electrode concentric with the central disc electrode. The middlering electrode may cover a first portion of the surface area of theelectrode substrate between a second radius and a third radius from thecenter point. The second radius may be greater than the first radius.The electrode device may also include an outer ring electrode concentricwith the central disc electrode and the middle ring electrode. The outerring electrode may cover a second portion of the surface area of theelectrode substrate between a fourth radius and a fifth radius from thecenter point. The fourth radius may be greater than the third radius andthe fifth radius defining an active area of the electrode substrate. Afirst distance between the fourth radius and the fifth radius may begreater than at least one of a second distance between the second radiusand the third radius or R.

In some embodiments, the central portion, the first portion, and thesecond portion together cover more than 50% of the active area of theelectrode substrate. The first portion or the second portion may covermore than 25% of the active area of the electrode substrate. The secondradius may be 2R, the third radius may be 3R, the fourth radius may be4R, and the fifth radius may be 9R. The second distance may be greaterthan R. The middle ring electrode may be a first middle ring electrode,and the electrode device may include a second middle ring electrodeconcentric with the central disc electrode. The second middle ringelectrode may be disposed on the electrode substrate covering a thirdportion of the surface area between a sixth radius and a seventh radiusfrom the center point. The seventh radius may be smaller than the fourthradius and the sixth radius may be greater than the third radius. Thefirst distance may be greater than a third distance between the sixthradius and the seventh radius. The first distance may be greater thanthe third distance and the third distance may be greater than the seconddistance. The third distance may be greater than the second distance andR. The second distance may be greater than R. The third distance may begreater than R.

Embodiments of the present disclosure may include an electrode device,including an electrode substrate having a surface area. The electrodedevice may include a central electrode disposed on the electrodesubstrate around a central portion of the surface area. The electrodedevice may also include a plurality of electrodes disposed on theelectrode substrate concentric with the central electrode. The pluralityof electrodes may include a first electrode covering a first portion ofthe surface area of the electrode substrate and a second electrodecovering a second portion of the surface area of the electrodesubstrate. The second portion may be greater than a combined surfacearea of the first portion and the central portion.

In some embodiments, the surface area of the electrode substrate mayextend to an outer periphery of the second electrode. The centralportion and the plurality of electrodes together may cover more than 50%of the surface area of the electrode substrate. The surface area of theelectrode substrate may extend to an outer periphery of the secondelectrode and the second portion may cover more than 25% of the surfacearea of the electrode substrate. The central electrode may be or includea disc covering a central region of the electrode substrate. A firstdistance between the first electrode and the second electrode may begreater than a distance between the central electrode and the firstelectrode. The electrode device may include a third electrode concentricwith the central electrode and the first electrode. The third electrodemay cover a third portion of the surface area of the electrode substrateand may be disposed on the electrode substrate between the firstelectrode and the second electrode.

Embodiments of the present disclosure may include a method of forming anelectrode device. The method may include forming a central electrode onan electrode substrate. The central electrode may have a first radius,“R” relative to a center point of the central electrode. The method mayinclude forming a middle electrode on the electrode substrate concentricwith the central electrode. The middle electrode may be disposed on theelectrode substrate between a second radius and a third radius from thecenter point. The second radius may be greater than the first radius.The method may also include forming an outer electrode on the electrodesubstrate concentric with the central electrode and the middleelectrode. The outer electrode may be disposed on the electrodesubstrate between a fourth radius and a fifth radius from the centerpoint. The fourth radius may be larger than the third radius. A firstdistance between the fourth radius and the fifth radius may be greaterthan at least one of a second distance between the second radius and thethird radius or R.

In some embodiments, the middle electrode is a first middle electrode.The method may include forming a second middle electrode on theelectrode substrate concentric with the central electrode. The secondmiddle electrode may be disposed on the electrode substrate between asixth radius and a seventh radius from the center point. The seventhradius may be smaller than the fourth radius. The method may includeconnecting the central electrode to a first terminal, connecting themiddle electrode to a second terminal, and the outer electrode to athird terminal. The method may include connecting the second middleelectrode to a fourth terminal. The outer electrode, the middleelectrode, and the central electrode may include an electrode surfacearea covering more than 50% of an active area of the electrodesubstrate. The outer electrode may cover more than 25% of the activearea of the electrode substrate. A distance between the middle electrodeand the outer electrode may be greater than a distance between thecentral electrode and the middle electrode.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a perspective view and a face view of an example aconcentric ring electrode (CRE), in accordance with some embodiments.

FIG. 2A illustrates a face view of an example structure of a tripolarCRE, in accordance with some embodiments.

FIG. 2B illustrates a face view of an example structure of a tripolarCRE, in accordance with some embodiments.

FIG. 2C illustrates a face view of an example structure of a quadripolarCRE, in accordance with some embodiments.

FIG. 3A illustrates a diagrammatic view of an example tripolar CRE, inaccordance with some embodiments.

FIG. 3B illustrates a diagrammatic view of an example tripolar CRE, inaccordance with some embodiments.

FIG. 3C illustrates a diagrammatic view of an example tripolar CRE, inaccordance with some embodiments.

FIG. 3D illustrates a diagrammatic view of an example quadripolar CRE,in accordance with some embodiments.

FIG. 3E illustrates a diagrammatic view of an example quadripolar CRE,in accordance with some embodiments.

FIG. 3F illustrates a diagrammatic view of an example pentapolar CRE, inaccordance with some embodiments.

FIG. 4A illustrates an example neurophysiological monitoring system, inaccordance with some embodiments.

FIG. 4B illustrates components of an example neurophysiologicalmonitoring system, in accordance with some embodiments.

FIG. 5 is a flow chart illustrating an example process for forming aCRE, in accordance with some embodiments.

FIG. 6 is a flow chart illustrating an example process for determining afunctional of an electrostatic potential measurable by a CRE, inaccordance with some embodiments.

FIG. 7 is a flow chart illustrating an example process for measuring aresponse signal by a CRE using a clinical system, in accordance withsome embodiments.

FIG. 8 illustrates examples of components of a computer system, inaccordance with some embodiments.

DETAILED DESCRIPTION

Noninvasive concentric ring electrodes (CREs) can improve significantlyon the performance of electroencephalography (EEG) systems. NoninvasiveCREs can estimate the surface Laplacian, the second spatial derivativeof the potentials on the scalp surface for EEG, directly at eachelectrode instead of combining the data from an array of conventional,single pole, disc electrodes. In particular, the disclosed electrodedevices, systems, and methods can improve accuracy ofelectrophysiological measurement using CREs.

CREs may also be arranged in arrays in order to monitor and/or map theLaplacian at different locations. Compared to EEG via disc electrodes,EEG via CREs has significantly better spatial selectivity,signal-to-noise ratio, and mutual information. CREs have foundapplications in a wide range of areas including brain—computerinterface, epileptic seizure onset detection, detection ofhigh-frequency oscillations and seizure onset zones, as well as inapplications involving electroenterograms, electrocardiograms (ECG), andelectrohysterograms. CREs could also be used for electrophysiologicalmonitoring, e.g. during surgery.

CRE systems have not made full use of variations in the CRE'sgeometrical configuration, such as the radii, spacing, and width of thering electrodes. Moreover, existing estimates for the Laplacian from CREmeasurements do not make optimal use of the information measured by theCRE.

The disclosed system and methods can improve over conventional systemsby improving accuracy of the surface Laplacian estimation, in light ofthe primary biomedical significance of such measurements. In particular,electrode devices and methods of using such electrode devices may reduceLaplacian estimation error by as much as three-fold, relative to typicalelectrode devices used for electrophysiological measurement thatincorporate concentric electrodes. Improved accuracy of Laplacianestimation, in turn, may provide improved health-outcomes including, butnot limited to, spatial localization of diagnostic measurements,observation of patient physiological functioning, or techniques forprolonged measurements without implantation of electrodes.

In a particular example, a CRE may include multiple recording surfaces,such as a central disc electrode and a pair of concentric ringelectrodes. The central disc electrode and the concentric ringelectrodes may be disposed on an electrode substrate. The active area ofthe CRE may be defined as the area within which the central disc and theconcentric rings are disposed. For example, in the case of concentricring electrodes, the outer radius of the outermost concentric ringelectrode may define the active area of the CRE. The electrodes may becoupled with leads and thereby connected to a signal receiving system.In some cases, the CRE may form a part of an array of CREs, positionedon a subject as part of measuring an electrophysiological signal. Theelectrodes may have differing widths, where the width may be defined bya difference between an outer radius and an inner radius of theelectrodes in the case of circular ring electrodes. In the case of thecentral disc electrode, the width may be considered to be the radius,“R.” Various configurations of the CRE include tripolar configurations,quadripolar configurations, pentapolar configurations, with variouswidth profiles, and varying distances between each consecutiveelectrode, also referred to as an inter-electrode spacing.

Accordingly, the disclosed systems can improve over conventional systemsand devices that measure electrostatic potentials by measuring thesepotentials more accurately through improved CRE electrodeconfigurations. Such improvements can provide improved patientexperiences including, but not limited to, shorter and/or less invasiveprocedures, as well as improved health outcomes such as improveddiagnostic and preventive measures. Moreover, the disclosed systems,devices, and methods may provide cost savings and efficiencyimprovements, for example, by enabling more accurate readings with fewerrecording sites and/or fewer electrodes. In particular, improvedelectrode configurations may provide cost improvements by obviating theneed to upgrade or replace existing CRE equipment.

I. Concentric Ring Electrode Configurations

FIG. 1 illustrates a perspective view and face view of an example CRE100, in accordance with some embodiments. The views presented in FIG. 1provide an illustrative example of a CRE incorporating multipleelectrodes that may be used for electrophysiological measurements withimproved accuracy. The CRE 100 may form a part of a measurement systemfor diagnostic measurement of patient nerve function. The configurationand number of electrodes of the CRE 100 may provide significantimprovements over state of the art electrodes, as described below. TheCRE 100 includes an electrode substrate 102, upon which a number ofrecording surfaces is formed. The recording surfaces may be or may bedefined at electrodes 104 a-d, which are disposed within an active area106 of the CRE 100. As shown, the active area 106 extends to the outeredge of an outermost electrode 104 d, and as such covers less surfacearea than the entire surface 112 of the electrode substrate 102. In someexamples, the surface area of the active area 106 may be coextensivewith the entire surface 112 of the electrode substrate 102. The activearea 106 is in-plane with the entire surface 112 of the electrodesubstrate 102. In some examples, however, the electrodes 104 may beformed having differing heights relative to the electrode substrate 102,may be flush with the electrode substrate 102, may be recessed into theelectrode substrate 102, or may be proud of the electrode substrate 102.

The CRE 100 includes a contact 108 housing leads 110. In some examplesthe contact 108 may include, but is not limited to, a fixed connectionto the leads 110 or a detachable connector facilitating removal of theelectrode substrate 102 from the leads 110. The leads 110 may beindividual connections or terminals electrically coupled to each of theelectrodes 104 and configured to apply or measure a voltage as part ofelectrophysiological measurement. In some embodiments, the electrodes104 and the leads 110 may be printed on a shared substrate 102, ondifferent layers of a multilayer substrate 102, or formed internal to acomposite substrate 102. The CRE 100 may be fabricated usingcircuit-printing techniques, lamination, additive manufacturing, orother approaches to form discrete recording surfaces (e.g., theelectrodes 104) within the active area 106.

As illustrated, the electrodes 104 are formed as concentric rings. Forexample, a central electrode 104 a may be formed on the electrodesubstrate 102, around which may be formed electrodes 104 b-d, such as afirst middle ring electrode 104 b, a second middle ring electrode 104 cand an outer ring electrode 104 d. The configuration, shape, and numberof the electrodes 104 of the CRE 100 provide improved performance forestimating the Laplacian of a voltage signal, which, in turn, improvesthe performance of the CRE 100 for electrophysiological measurements.For example, the central electrode 104 a may be a disc, a ring, oranother shape, such that it is symmetric about a central point of theactive area 106.

As described in more detail in reference to FIGS. 2-3, below, the CRE100 may include three electrodes 104 (a tripolar configuration), fourelectrodes 104 (a quadripolar configuration), five electrodes 104 (apentapolar configuration), or more. In some embodiments, the size andposition of the electrodes 104 are such that one or more generalprinciples of CRE 100 configuration are satisfied. For example, thecentral electrode 104 a and the concentric electrodes 104 b-d may beformed such that an inter-electrode spacing between the electrodes 104is minimized within the constraints of the physiological application,where the spacing may be described by a separation between the outeredges of adjacent electrodes 104 or by a distance between the electrodes104 as measured from a center radius of adjacent electrodes 104. Forexample, salt bridging between the electrodes 104 caused by ions in oron a surface on which the CRE 100 is placed, such as the skin of apatient, may result in coupling between the electrodes 104. In this way,a minimum inter-electrode distance may be greater than or about 0.01 mm,greater than or about 0.1 mm, greater than or about 0.5 mm, greater thanor about 1 mm, greater than or about 5 mm, or greater.

Similarly, the CRE 100 may include electrodes 104 having a minimumradius and minimum width, except for the outer ring electrode 104 d. Inthe context of electrode dimensions, a minimum radius and minimum widthmay describe the dimensions forming a contact area for measuringelectrophysiological signals. For example, the minimum radius may berelated to the minimum spacing between the electrodes 104 and theminimum width of each of the electrodes 104 for which signal strengthpermits accurate measurement. Signal strength may describe a signal tonoise ratio such that a periodic electrophysiological signal may beaccurately measured (e.g., ECG, EEG signals, etc.). Similar to thediscussion regarding minimum inter-electrode spacing, the dimensions ofthe electrodes 104 may depend at least in part on physiologicalcharacteristics of the subject as well as the type of measurement beingperformed. As such, different configurations of the CRE 100 may bebetter suited to some measurements than others, with the understandingthat a larger active area 106 may include larger electrodes 104, and inturn may measure a stronger electrophysiological signal. Balancing this,however, is spatial resolution of measurements using the CRE, whichtends to favor a smaller active area 106 in applications for measuringspecific electrophysiological signals within a region having multipleperiodic systems or within a space restriction (e.g., sensors forpediatric applications). In some embodiments, the active area 106 may becircular with a diameter greater than or about 5 mm, greater than orabout 10 mm, greater than or about 20 mm, greater than or about 30 mm,greater than or about 40 mm, greater than or about 50 mm, greater thanor about 60 mm, greater than or about 70 mm, greater than or about 80mm, greater than or about 90 mm, greater than or about 100 mm, orgreater. As described in more detail in reference to FIG. 3, rather thanbeing described explicitly in terms of spatial dimensions, thedimensions of the electrodes 104 may be described in terms of fractionalcoverage of the active area 106 or in terms of multiples of a radius ofthe central electrode 104 a.

In some embodiments, the electrodes 104 may have differing widths, whichmay provide improved performance. For example, increasing the width ofan electrode 104 closer to the outer edge of the active area 106 may beadvantageous to increasing the width of an electrode 104 closer to thecentral electrode 104 a in the context of Laplacian estimation error. Asan illustrative example, the central electrode 104 a may be a disc ofradius “R,” the first middle ring electrode 104 b, between an innerradius and an outer radius, may be wider than R, the second middle ringelectrode 104 c may be wider than the first middle ring electrode 104 b,and the outer ring electrode 104 d may be wider than the second middlering electrode 104 c. In some embodiments, one or more of the middlering electrodes 104 b-c may be wider than either the central electrode104 a or the outer ring electrode 104 d.

In some embodiments, increasing the distance between the electrodes 104closer to the outer edge of the active area 106 may provide improvedelectrophysiological measurement, relative to configurations withincreasing distance between the electrodes 104 closer to the centralelectrode 104 a. As described in more detail in reference to FIGS.3A-3F, the electrodes 104 may be separated by a variable inter-electrodespacing. In some cases, the inter-electrode spacing may increase witheach consecutive concentric electrode. For example, the outer ringelectrode 104 d may be spaced farther from the outer edge of the secondmiddle ring electrode 104 c than the inner edge of the second middlering electrode 104 c is spaced from the outer edge of the first middlering electrode 104 b. In some cases, the spacing may increasenon-linearly according, for example, to a spacing function (e.g., ageometric function, a quadratic function, a cubic function, a sigmoidalfunction, an exponential function, etc.).

In some embodiments, the electrodes 104 account for a portion of theactive area 106 greater than or about 45%, greater than or about 50%,greater than or about 55%, greater than or about 60%, greater than orabout 65%, greater than or about 70%, greater than or about 75%, orgreater, of the total active area 106. In some cases, the outer ringelectrode 104 d, the second middle ring electrode 104 c, or the firstmiddle ring electrode 104 b may individually cover about 25% or more,about 30% or more, about 35% or more, about 40% or more, about 45% ormore, about 50% or more, or a larger portion of the active area 106.

While the CRE 100 is illustrated as a quadripolar electrode, embodimentsof the present disclosure also include other electrode configurations.In some embodiments, the alternative configurations may similarly bedescribed by characteristics described in reference to the CRE 100. Forexample, the electrode configurations described in the followingparagraphs may include fewer electrodes than the CRE 100 that maynonetheless cover more than 50% of the corresponding active area of theelectrode substrate. Similarly, other CRE configurations may alsoinclude varying inter-electrode spacing, as described in more detail inreference to FIGS. 2A-2C and FIGS. 3A-3F, below.

FIG. 2A illustrates a face view of an example structure of a tripolarCRE 200, in accordance with some embodiments. The CRE 200 is an exampleof the CRE 100. The CRE 200 includes multiple recording surfaces, suchas a central electrode 202, a middle ring electrode 204, and an outerring electrode 206. In some embodiments, these recording surfaces may becomposed of one or more metals or conductive materials, including butnot limited to silver, gold, copper, tin, aluminum, silver chloride, orany other conductor. In some embodiments, the recording surfaces mayalso contain other materials, such as non-conducting materials. Therecording surfaces may be separated by dielectrics, such as empty spaceor air, or any other dielectric or insulating material. In someembodiments, the CRE 200 may be removably affixed to, or contact, apatient's head or scalp, to perform EEG. In particular, the CRE 200 maymeasure the surface Laplacian, or the second spatial derivative, of theelectrostatic potential on the patient's scalp surface. In variousembodiments, CRE 200 may be used for brain-computer interfaces,epileptic seizure onset detection, detection of high-frequencyoscillations, which may typically predict or precede seizures, andseizure onset zones, as well as in applications involvingelectroenterograms, ECG, electrohysterograms, or any other kind ofelectrophysiological monitoring, e.g. during surgery.

In some embodiments, the CRE 200 may be used to measure the electricpotential at the recording surfaces, or an average of the potential overthe areas of the respective recording surfaces. In some embodiments, themeasured ring potentials may be relative to a reference potential suchas the central disc potential, for example the respective potentialsassociated with the concentric electrodes 204 and 206 may be measuredand/or expressed as differences from the potential of the centralelectrode 202. In turn, these potential measurements may be used toestimate a surface Laplacian, or second spatial derivative, given inpolar coordinates for a radially symmetrical CRE configuration as

${{\Delta v_{0}} \equiv {( {\frac{\partial^{2}}{\partial r^{2}} + {\frac{1}{r}\frac{\partial}{\partial r}} + {\frac{1}{r^{2}}\frac{\partial^{2}}{\partial\theta^{2}}}} )v_{0}}},$

of the electric potential v₀, near the center of the CRE 200 or thecentral electrodes 202. The potentials or potential differences may alsobe referred to as voltages. Note that the spatial coordinates r and θrepresent coordinates in the plane of the CRE 200. For example, if theCRE 200 is configured parallel to a patient's scalp in order to measurethe surface Laplacian along the scalp, the rθ-plane may be parallel tothe scalp.

FIG. 2B illustrates a face view of an example structure of a tripolarCRE 220, in accordance with some embodiments. The CRE 220 is an exampleof the CRE 200. In this example, the central electrode 222 is similar inradius as the central electrode 202 of the example of FIG. 2A, but thering electrodes 224 and 226 vary in size relative to the ring electrodes204 and 206 of FIG. 2A. As a result, the ratios of various geometricalfeatures of CRE 220 differ from those of CRE 200 in FIG. 2A. Forexample, the thickness of the outer ring electrode 226 is greater forCRE 220 than for CRE 200. Similarly, in this example, theinter-electrode separations may be considered to vary for CRE 220because the radial separation from ring electrode 224 to the outerperiphery of central electrode 222 may be greater than the radialseparation between ring electrode 226 and ring electrode 224. Bycontrast, CRE 200 in the example of FIG. 2A may have constantinter-electrode spacing. The inter-electrode spacing may also bereferred to herein as inter-electrode distances or intervals.

In some embodiments, the disclosed system and methods may make use ofsuch geometrical or other variations to provide improved accuracy andprecision of physiological measurements. For example, the ring radii,width, or inter-electrode spacings may affect the measurementperformance, sensitivity, and/or accuracy of the CRE. Electrodeconfigurations may also improve the accuracy of measurement of thesurface Laplacian. Such improvements may lead to improved patientexperiences such as shorter procedures, as well as to improved healthoutcomes. Moreover, the disclosed system may provide cost savings, forexample, by enabling accurate readings with less equipment.

Other variations are also possible, such as: geometrical variations(e.g., using non-concentric or non-circular rings, or otherwise varyingthe sizes, separations, number, or shapes of recording surfaces);material or composition variations (e.g., using different metals oralloys for the recording surfaces, varying the materials of differentrecording surfaces within a single CRE, etc.); or other variations, andare not limited by the present disclosure. Electrode configurationsdescribed herein may improve estimation of a potential Laplacian, and/oroptimize other aspects of methods for estimating the Laplacian, or otherelectrical characteristics measured by the CRE, as described hereinbelow.

FIG. 2C illustrates a face view of an example structure of a quadripolarCRE 240 with three concentric electrodes, in accordance with someembodiments. The CRE 240 is an example of the CRE 200. In this example,a central disc electrode 242 serves as the central electrode. WhileFIGS. 2A-2C illustrate examples of CREs having a central disc electrode,some embodiments include a central electrode that is not circular. Forexample, the central electrode may be polygonal, or may be oblong, suchthat it is centered and symmetric about a source location for anelectrophysiological signal. The central disc electrode 242, and twoinner ring electrodes 244 and 246 of CRE 240 have similar sizes, shapes,and separations compared with the central disc 202 and rings 204 and 206of CRE 200 in the example of FIG. 2A. However, CRE 240 also includes anadditional ring electrode 248, for a total of three ring electrodes, orfour recording surfaces including the central disc electrode 242.

In some examples, CREs with additional recording surfaces, such asadditional ring electrode 248, may have improved measurementperformance, sensitivity, and/or accuracy. In an example, an estimate ofthe surface Laplacian of the electrostatic potential near the centraldisc electrode 242 or the center of the CRE may improve systematicallyas the number of concentric electrodes is increased. In someembodiments, the CRE can have any number of concentric electrodes, andis not limited by the present disclosure. However, in order to makeoptimal use of the additional recording surfaces, the system may combinethe measured potentials based on a formula and/or coefficients that areoptimized for the particular geometry of the CRE. Thus, in general, theformula and/or set of coefficients may depend on the number n ofconcentric electrodes.

For example, the system may make use of a different set of coefficientsfor a CRE with n rings than it does for a CRE with a different number mof rings. For example, coefficients associated with the inner ringelectrodes 244 and 246 of quadripolar CRE 240 may differ from therespective coefficients associated with electrodes 204 and 206 of thetripolar CRE 200 of FIG. 2A. Of course, the system can also use acoefficient associated with outermost ring electrode 248 of quadripolarCRE 240, which has no counterpart ring in tripolar CRE 200. Moreover, insome embodiments, such a coefficient associated with outermost ring 248may also differ from the coefficient associated with outer ringelectrode 206 of the tripolar CRE 200, even though the outer ringelectrode 206 is the outermost concentric electrode of CRE 200.

FIG. 3A illustrates a diagrammatic view of an example tripolar CRE 300,in accordance with some embodiments. As described in reference to FIGS.1-2B, above, the tripolar CRE 300 includes a central electrode 310having a radius, “R,” a first electrode 312, and a second electrode 314.The first electrode 312 and second electrode 314 are illustrated assections for simplicity of explanation, but describe electrodes centeredconcentrically around the central electrode 310. A de-dimensionalizedcoordinate system 320, defined in reference to the radius R of thecentral electrode 310 is provided to permit the direct comparison ofmultiple different CRE configurations, without regard to overall size ofthe CREs that may differ for different applications. For simplicity incomparison, each example CRE configuration presented in FIG. 3A-3F aredescribed with the same de-dimensionalized coordinate system 320,although it is understood that other relative dimensions arecontemplated for different CRE configurations. In FIG. 3A, the tripolarCRE 300 includes constant inter-electrode spacing, with the firstelectrode 312 covering between approximately 4R-5R, and the secondelectrode 314 covering between approximately 8R-9R. The CREconfiguration illustrated in FIG. 3A corresponds to a constant-distancearrangement, which may result in higher error when estimating theLaplacian of surface potentials. The CRE configuration of FIG. 3A is butone example embodiment, where many other possible configurations arecontemplated herein.

Alternative tripolar CRE configurations may include, but are not limitedto, those described in Table 1, below. For integer values of eachparameter, a tripolar CRE with an outer radius of 9R may have 70different configurations, of which 12 are summarized in Table 1. In someembodiments, some configurations provide improved estimation errorrelative to other configurations. For example, in Table 1, CREconfiguration number 6 may be characterized by an error as much as 100%higher than configuration number 1, while configuration number 2 may becharacterized by an error only as much as 1% higher than configurationnumber 1. In this way, configurations that conform to the principlesdescribed in reference to FIG. 1 may provide improved Laplacianestimation, and thus may improve overall performance forelectrophysiological measurements.

TABLE 1 First Second Central Electrode 312 Electrode 314 ConfigurationElectrode 310 Inner Outer Inner Outer Number Radius, R Radius RadiusRadius Radius 1 1 2 3 4 9 2 1 2 3 5 9 3 1 2 3 6 9 4 1 2 3 7 9 5 1 2 3 89 6 1 3 4 8 9 7 1 4 5 8 9 8 4 5 7 8 9 9 2 6 7 8 9 10 3 6 7 8 9 11 4 6 78 9 12 5 6 7 8 9

FIG. 3B illustrates a diagrammatic view of an example tripolar CRE 301,in accordance with some embodiments. In contrast to the CREconfigurations described in reference to FIG. 3A, CRE 301 includes arelatively wide first electrode 330 and a relatively narrow secondelectrode 332. In the tripolar CRE 301, the first electrode 330 ispositioned to cover between 2R-6R, while the second electrode 332 ispositioned to cover between 8R-9R. As such, the first electrode 330 maycover as much as 30% or more, as much as 40% or more, 50% or more, 60%or more, or more of the active area of the CRE, 81πR², that is boundedby the outer radius of the second electrode 332.

FIG. 3C illustrates a diagrammatic view of an example tripolar CRE 303,in accordance with some embodiments. Similar to the tripolarconfiguration described in reference to FIG. 3B, the tripolar CRE 303includes a relatively narrow first electrode 340 and a relatively widesecond electrode 342. In such configurations, the second electrode 342may cover as much as 20% or more, 25% or more, 30% or more, 40% or more,50% or more, 60% or more, or more of the active area of the CRE 303. Forexample, as illustrated, the first electrode 340 covers between 2R-3Rand the second electrode 342 covers between 4R-9R. As such, the secondelectrode 342 covers as much as 90% of the active area of the CRE 303.While the CRE 303 includes constant inter-electrode spacing, tripolarCREs are not limited to integer R values of inter electrode spacing. Forexample, a CRE may include an inter-electrode spacing of between 0-R,between R-2R, between 2R-3R, or larger, depending on the extent of theactive area (e.g., where the radius of the active area is larger than9R).

FIG. 3D illustrates a diagrammatic view of an example quadripolar CRE305, in accordance with some embodiments. As described in reference toFIG. 1, above, and FIG. 2C, above, the quadripolar CRE 305 may include athird electrode 350, positioned between a first electrode 352 and asecond electrode 354 of a tripolar configuration. Quadripolar CREs mayprovide improved Laplacian estimation relative to tripolar CREs, sinceLaplacian estimation error corresponds to truncation error of a Taylorseries expansion. Additional ring electrodes (e.g., quadripolar asopposed to tripolar or bipolar configurations) permit additionaltruncation terms to be cancelled, which in turn decreases the truncationerror. As shown, similar variation in electrode width and spacing may beincluded in quadripolar CRE configurations as seen in tripolar CREconfigurations. For example, the first electrode 352 of CRE 305 coversbetween 2R-3R on the active area, the third electrode 350 covers between4R-5R on the active area, and the second electrode 354 covers between6.2R-9R of the active area, where the active area is bounded by theouter radius of the second electrode 354, 9R. As illustrated in FIG. 3D,the second electrode 354 has a non-integer width. In the configurationshown, the second electrode 354 covers approximately 53% of the activearea (81πR²). In some embodiments, the second electrode 354, the firstelectrode 352, or the third electrode 350 may cover as much as 25% ormore, 30% or more, 35% or more, 40% or more, 50% or more, 55% or more,or a larger portion of the active area of the quadripolar CRE 305.

FIG. 3E illustrates a diagrammatic view of an example quadripolarconcentric ring electrode 307, in accordance with some embodiments. Asan illustrative example of another quadripolar CRE having a relativelywide third electrode 362, the CRE 307 includes a third electrode 362covering between 3.8R-6.8R, a second electrode 364 covering between7.5R-9R, and a first electrode 360 covering between 2R-3R. In thisexemplary configuration, the third electrode 362 covers approximately40% of the active area of the CRE 307, while total coverage of therecording surfaces, made up of all three electrodes and the centralelectrode 310, is approximately 76% of the active area of thequadripolar CRE 307 (81πR²) bounded by the outer radius of the secondelectrode 364.

FIG. 3F illustrates a diagrammatic view of an example pentapolar CRE309, in accordance with some embodiments. Not being limited only totripolar CREs and quadripolar CREs, embodiments of the presentdisclosure include CRE configurations including additional electrodesincluding four concentric electrodes, five concentric electrodes, sixconcentric electrodes, or more. As illustrated in FIG. 3F, thepentapolar CRE 309 includes a first electrode 370, a second electrode372, a third electrode 374, and a fourth electrode 376, each concentricwith the central electrode 310. The third electrode 374 and fourthelectrode 376, in keeping with the numbering convention used fortripolar CREs, may be disposed on an electrode substrate (e.g.,electrode substrate 102 of FIG. 1) between the first electrode 370 andthe second electrode 372. In pentapolar configurations, as withconfigurations including fewer electrodes, each electrode may have adifferent width. As illustrated, the electrodes may progressivelyincrease in width with increasing distance from the central electrode310. For example, in the CRE 309 the first electrode 370 has a widthless than R, the third electrode 374 has a width slightly greater thanR, the fourth electrode 376 has a width slightly less than 2R, and thesecond electrode 372 has a width larger than 2R. In this example, therecording surfaces cover as much as 82% of the active area of the CRE(81πR²). By providing concentric electrodes with different widths,however, the recording surfaces may cover portions of the active areaexceeding 30% or more, 40% or more, 50% or more, 55% or more, 65% ormore, 70% or more, 75% or more, 80% or more, 85% or more, or larger.

While the preceding descriptions focus on CRE configurations for whichthe active area of the CRE is 81πR², corresponding to an outer radius of9R, embodiments of the present disclosure include CREs with differingnumbers of concentric electrodes, for which the outer radius of theactive area may be larger than 9R or less than 9R, in integer multiplesor non-integer multiples of R. Descriptions using R as a referentialdimension are provided for simplicity of description and to generalizethe application of the configurations described herein to multiplescales where the outer radius of the CRE is as much as 1 mm or larger, 1cm or larger, or 10 cm or larger. In some embodiments, therefore, R maycorrespond to 1.1 mm for a CRE having an outer radius of 10 mm dividedinto nine intervals of R. As another example, for a CRE having an outerradius of 1.5 cm, divided into 100 intervals of R, R will correspond toa length of 0.15 mm.

II. Estimating Laplacian Via Finite Dimensions Model (FDM)

In some embodiments, the Laplacian of a CRE may be estimated for theelectrode configurations described in reference to FIG. 1, FIGS. 2A-C,and FIGS. 3A-F. The Laplacian may be described as the spatial derivative

${\Delta\; v_{0}} \equiv {( {\frac{\partial^{2}}{\partial x^{2}} + \frac{\partial^{2}}{\partial y^{2}}} )v_{0}\mspace{14mu}{or}\mspace{14mu}\Delta\; v_{0}} \equiv {( {\frac{\partial^{2}}{\partial r^{2}} + {\frac{1}{r}\frac{\partial}{\partial r}} + {\frac{1}{r^{2}}\frac{\partial^{2}}{\partial\theta^{2}}}} )v_{0}}$

(also denoted as ∇²v₀) of the electrostatic potential v₀ near the centerof a (n+1)-polar CRE with n concentric electrodes. In some embodiments,the system may apply a finite dimensions model (FDM), which considersmultiple electrode parameters including, but not limited to, the radiusof the central electrode 310 and the individual widths of concentricelectrodes, to estimate the Laplacian. The FDM may treat the centralelectrode and concentric rings of the CRE as solid conductors to improveLaplacian error estimation over alternative methods, such as thenegligible dimensions model. As illustrated in FIGS. 3A-F, CREs mayinclude, but are not limited to, linearly increasing inter-ringdistances, constant inter-ring distances configurations, linearlydecreasing inter-ring distances, or configurations incorporating anon-linear separation progression. The FDM may describe electrodeconfigurations in terms of a single CRE radius subdivided into a numberof equal intervals, such as nine equal intervals. The central electrodeand each concentric ring electrode may thus be described by an innerradius and an outer radius in reference to the radius “R,” while thetotal active area of the CRE may be described as 81πR². As one potentialapproach, an average potential on each electrode may be calculated usingHuiskamp's Laplacian potential derivation based on the Taylor seriesexpansion.

In some embodiments, this Laplacian estimate signal may be calculatedusing a custom preamplifier board, and may be sent to the clinicalamplifier for each CRE. Alternatively, the Laplacian estimate may becalculated via a special- or general-purpose circuit or computer, asoftware module, or any other device, and is not limited by the presentdisclosure.

III. System

FIG. 4A illustrates an example neurophysiological monitoring system 400,according to at least one example. The neurophysiological monitoringsystem 400 includes a monitoring system including a controller 402 and acomputing device 404, and a display system including a display device406. The controller 402 and the display device 406 may be electronicallyconnected to the computing device 404 in any suitable manner (e.g.,network cables, wireless networks, optical cables, power cables,input/output interfaces, etc.).

Generally, the computing device 404, which may be any suitable computingdevice, is configured to manage the operation of the controller 402 andgenerate and provide information for presentation at the display device406. The controller 402, operating under at least partial control of thecomputing device 404, may be configured to generate, deliver, detect,and/or process electrical signals with respect to a patient 408, such asa patient undergoing EEG, brain-computer interfaces, seizure onsetdetection, detection of high-frequency oscillations and seizure onsetzones, as well as in applications involving electroenterograms,electrocardiograms (ECG), electrohysterograms, or any other kind ofelectrophysiological monitoring. In particular, a CRE may measure thesurface Laplacian, or the second spatial derivative, of theelectrostatic potential on the patient's scalp surface. Thus, thecontroller 402 may be an example of a multimodal machine forsimultaneous signal generation, detection, and recording. Such signalsmay be referred to as neurological data or electrophysiological data. Insome examples, the controller 402 may receive commands from thecomputing device 404 to send electrical signals to the patient 408.Response signals may be detected or generated by the patient 408 inresponse to electrical signals from the controller 402. These responsesignals are passed by the controller 402, which may perform somefiltering and/or processing, to the computing device 404. The computingdevice 404, executing monitoring modules (e.g., dedicated hardware,firmware, or software), may be configured to receive, augment, and/orotherwise process the response signals prior to providingrepresentations of the response signals for presentation at the displaydevices 406. The modules of the computing device 404 may allowsimultaneous viewing of multiple tests. In some examples, the tests areviewed on the display device 406.

The system may monitor and/or stimulate the patient 408, e.g. forseizure detection and/or control or brain-computer interface, via one ormore electrodes 410 a, 410 b, such as a CRE (e.g., CRE 100 of FIG. 1).The monitoring may occur as electrical signals that are introduced atthe second electrode 410 b and then detected by the first electrode 410a. In some embodiments, a plurality of CREs may also be arranged inarrays, such as regular arrays, in order to monitor and/or map out theLaplacian of the potential at different locations on or near a patient.Note that, using coefficients and/or a formula as disclosed herein, anindividual CRE or each respective CRE in an array may measure theLaplacian directly, thereby reducing the computational burden for system400 and/or a separate computer to compute the Laplacian. In someembodiments, such an array may be rectangular. In some embodiments, thedisclosed system can also interpolate between the individual CREs in anarray, in order to obtain a more detailed map of the potential and/orthe Laplacian.

In some examples, the patient 408 may be situated on an operating table412. The operating table 412 may be fixed or mobile, and may includeadjustability. In some examples, the operating table 412 may includegrounding connections, adapters for supporting the electrodes 410 and/orcomponents of the controller 402.

In some embodiments, the display device 406 may be positioned away fromthe patient 408. For example, the display device 406 may be supported bya table 418. The display device 406 may be electronically and/orphysically connected to the computing device 404. For example, thecomputing device 404 may be a laptop and the display device 406 may be amonitor of the laptop.

In some examples, the positioning of the display device 406 may berelative to a user 416 such as a clinically trained and certifiedtechnologist. For example, the display device 406 may be positioned suchthat a display surface of the display device 406 is viewable (e.g.,within a field of view) by the user 416.

FIG. 4B illustrates components of an example neurophysiologicalmonitoring system 450, according at least one example. Theneurophysiological monitoring system 450 is an example of theneurophysiological monitoring system 400 described herein. Thus, theneurophysiological monitoring system 450 includes a display system 452and a monitoring system 454. Like the display system described withreference to FIG. 4A, the display system 452 includes one or moredisplay devices such as display devices 456. Like the display devices406, the display devices 456 may be any suitable device capable ofvisually presenting information. Examples of such devices may includecathode ray tube (CRT) displays, light-emitting diode (LED) displays,electroluminescent displays (ELD), electronic paper, plasma displaypanels (PDP), liquid crystal displays (LCD), organic light-emittingdiode (OLED) displays, surface-conduction electron-emitter displays(SED), field emission displays (FED), projectors (LCD, CRT, digitallight processing (DLP), liquid crystal on silicon (LCoS), LED, hybridLED, laser diode), and any other suitable device capable of displayinginformation. The display devices 456 may be positioned adjacent to theusers 416.

The monitoring system 454 is an example of the monitoring systemdescribed with reference to FIG. 4A. To this end, the monitoring system454 may include the computing device 404, the controller 402, and one ormore attachment devices 457. The attachment devices 457 may be connectedto the controller 402 in order to augment or otherwise enable certainfunctions of the controller 402. In some examples, the attachmentdevices 457 are themselves separate modules that are disposed betweenthe controller 402 and the patient 408. The function of the exampleattachment devices 457 will be discussed later. Though a few examples ofattachment devices 457 are illustrated, other and different attachmentdevices 457 may also be connected to the controller 402.

In various embodiments, either the controller 402 or the computingdevice 404 may store the linear combination coefficients for thepotentials measured by the CRE. For example, an amplifier orpreamplifier 464 included in or associated with controller 402 may beconfigured to calculate a Laplacian estimate from the potentials basedon the coefficients. In some embodiments, the system 400 (such ascontroller 402 or computing device 404) may receive and store thecoefficients.

In some embodiments, the controller 402 may include an electricalstimulator 458 and one or more input/output interfaces 460. Theelectrical stimulator 458 may include a wide variety of triggering modesand pulse outputs to provide electrical stimulation for a patient'snervous system. In some examples, the system may instead measure,detect, and/or image a patient or a target signal, such as an EEGsignal, without stimulating the patient or target.

The attachment devices 457 also include one or more preamplifiers 464.The preamplifiers 464 are examples of digital preamplifier modules. Insome examples, the preamplifiers 464 provide signal detection,amplification, montage selection, A/D conversion, antialiasingfiltering, and digital signal processing. The preamplifiers 464 mayroute detected signals to the controller 402 via any suitableconnection. Each preamplifier 464 may include inputs for the electrodes410, such as a CRE and/or the recording sites of a CRE. Thepreamplifiers 464 may calculate a Laplacian estimate signal based onlinear combination coefficients computed as disclosed herein.

The computing device 404 may be in communication with the othercomponents of the neurophysiological monitoring system 450 via one ormore network(s), wired connections, and the like. The network mayinclude any one or a combination of many different types of networks,such as cable networks, the Internet, wireless networks, cellularnetworks, radio networks, and other private and/or public networks.

Turning now to the details of the computing device 404, the computingdevice 404 may include at least one memory 468 and one or moreprocessing units (or processor(s)) 470. The processor(s) 470 may beimplemented as appropriate in hardware, computer-executableinstructions, software, firmware, or combinations thereof. For example,the processors 470 may include one or more general purpose computers,dedicated microprocessors, or other processing devices capable ofcommunicating electronic information. Examples of the processors 470include one or more application-specific integrated circuits (ASICs),field programmable gate arrays (FPGAs), digital signal processors (DSPs)and any other suitable specific or general purpose processors.

Computer-executable instruction, software, or firmware implementationsof the processor(s) 470 may include computer-executable ormachine-executable instructions written in any suitable programminglanguage to perform the various functions described. The memory 468 mayinclude more than one memory and may be distributed throughout thecomputing device 404. The memory 468 may store program instructions(e.g., a monitoring module 472) that are loadable and executable on theprocessor(s) 470, as well as data generated during the execution ofthese programs. Depending on the configuration and type of memoryincluding the monitoring module 472, the memory 468 may be volatile(such as random access memory (RAM)) and/or non-volatile (such asread-only memory (ROM), flash memory, or other memory). In someembodiments, the monitoring module 472 may receive and/or adjust thelinear combination coefficients for Laplacian estimation based on thepotentials measured by the CRE. In some embodiments, monitoring module472 may implement the linear combination based on these coefficients.The computing device 404 may also include additional removable storage478 and/or non-removable storage including, but not limited to, magneticstorage, optical disks, and/or tape storage. The disk drives and theirassociated computer-readable media may provide non-volatile storage ofcomputer-readable instructions, data structures, program modules, andother data for the computing devices. In some implementations, thememory 468 may include multiple different types of memory, such asstatic random access memory (SRAM), dynamic random access memory (DRAM),or ROM. The memory 468 may also include an operating system 474.

The memory 468 and the additional storage 478, both removable andnon-removable, are examples of computer-readable storage media. Forexample, computer-readable storage media may include volatile ornon-volatile, removable, or non-removable media implemented in anysuitable method or technology for storage of information such ascomputer-readable instructions, data structures, program modules, orother data. As used herein, modules may refer to programming modulesexecuted by computing systems (e.g., processors) that are part of themonitoring module 472. The modules of the monitoring module 472 mayinclude one or more components, modules, and the like. For example,monitoring module 472 may include modules or components that receive,adjust, and/or implement the linear combination coefficients forLaplacian estimation based on the potentials measured by the CRE. Thecomputing device 404 may also include input/output (“I/O”) device(s)and/or ports 476, such as for enabling connection with a keyboard, amouse, a pen, a voice input device, a touch input device, a display,speakers, a printer, or other I/O device. The I/O device(s) 476 mayenable communication with the other systems of the neurophysiologicalmonitoring system 450.

The computing device 404 may include a user interface 480. The userinterface 480 may be utilized by an operator or other authorized usersuch as the user 416 to access portions of the computing device 404(e.g., the monitoring module 472). In some examples, the user interface480 may include a graphical user interface, web-based applications,programmatic interfaces such as application programming interfaces(APIs), or other user interface configurations.

IV. Processes

FIGS. 5 and 6 illustrate example flow diagrams showing processes 500 and600, as described herein. The processes 500, and 600 are illustrated aslogical flow diagrams, each operation of which represents a sequence ofoperations that can be implemented in hardware, computer instructions,or a combination thereof. In the context of computer instructions, theoperations represent computer-executable instructions stored on one ormore computer-readable storage media that, when executed by one or moreprocessors, perform the recited operations. Generally,computer-executable instructions include routines, programs, objects,components, data structures, and the like that perform particularfunctions or implement particular data types. The order in which theoperations are described is not intended to be construed as alimitation, and any number of the described operations can be omitted orcombined in any order and/or in parallel to implement the processes.

Additionally, some, any, or all of the processes may be performed underthe control of one or more computer systems configured with executableinstructions and may be implemented as code (e.g., executableinstructions, one or more computer programs, or one or moreapplications) executing collectively on one or more processors, byhardware, or combinations thereof. As noted above, the code may bestored on a computer-readable storage medium, for example, in the formof a computer program comprising a plurality of instructions executableby one or more processors. The computer-readable storage medium isnon-transitory.

A. Process for Forming CRE

FIG. 5 is a flow chart illustrating an example process 500 for forming aCRE (e.g., CRE 100 of FIG. 1), according to embodiments. In someembodiments, multiple CREs may be formed via the process disclosedherein, for example an array of CREs. In some embodiments, forming theCRE may involve forming one or more parts of the CRE, such as therecording surfaces (e.g., electrodes 104 of FIG. 1), either separatelyor jointly. In an exemplary embodiment, at block 505, forming process500 may include forming a central electrode (e.g., electrode 104 a ofFIG. 1) on a non-conductive or insulating substrate (e.g., electrodesubstrate 102 of FIG. 1). The substrate may be rigid (e.g., gold-platedcopper on biocompatible dielectric) or flexible (e.g., polyester film,or silver paste on polyester film) in order to be mounted and/or contacta monitoring target, such as a patient. In some embodiments, thesubstrate may be designed to provide a consistent contact potential withthe target, as well as to fit the target's form. In particular, flexiblesubstrates may improve the CRE's ability to adjust to body contours forbetter contact and to provide higher signal amplitude andsignal-to-noise ratio. In various embodiments, the CRE may bebiocompatible, wireless, battery-powered, and/or disposable. The centralelectrode (e.g., central electrode 104 a of FIG. 1), may be circularlysymmetric, and, as such, may be or include a disc or a ring.

At block 510, the process 500 may include forming a middle electrode onthe substrate (e.g., electrode 104 b of FIG. 1). In some examples, thismay include depositing, printing, and/or securing the middle electrodeto the substrate. In various embodiments, the middle electrode may bepre-formed, or may be formed on the electrode substrate as part of theforming process. For example, the central electrode and middle electrodeof the CRE may be printed via screen printing, inkjet, and/or gravuretechniques onto the electrode substrate.

At block 515, the process 500 may optionally include forming one or moreadditional middle electrodes (e.g., electrode 104 c of FIG. 1).Similarly to the operations of block 510, block 515 may include formingone or more additional middle electrodes by disposing pre-formedelectrodes concentric with the middle electrode and the centralelectrode. When printing or engraving the electrodes, however, block505, block 510, and block 515 may occur together, such that portions ofthe concentric electrodes and the central electrode may be formedconcurrently. In this way, the process 500 may also include block 520,where an outer electrode (e.g., electrode 104 d of FIG. 1) may be formedon the electrode substrate. As with block 515, the outer electrode maybe pre-formed and disposed on the electrode substrate, in which case theouter electrode may be formed concurrently with or separately from theother electrodes of the CRE. Similarly, when the process 500 includesprinting or engraving to form the electrodes, the block 520 may beconcurrent with the block 505, block 510, and block 515, as when theelectrodes are formed by patterning a substrate, followed by selectivedeposition of a metal film onto regions of the substrate to form theelectrodes.

The electrodes may be formed such that the central electrode is circularand had a radius of R. In such cases, the middle electrode may be a ringelectrode, and have an inner radius of 2R and an outer radius of 3R. Insuch cases the outer electrode may also be a ring electrode and may havean inner radius of 4R and an outer radius of 9R. In some examples, themiddle electrode may be narrower than the outer electrode. In someexamples, the outer electrode may be wider than the radius of thecentral electrode, R. In some examples, the middle electrode may becloser to the central electrode than to the outer electrode, which maybe measured by a smaller inter-electrode spacing between the centralelectrode and the middle electrode than between the middle and the outerelectrodes. In some examples, the outer electrode, the middle electrode,and the central electrode may include an electrode surface area coveringmore than 50% of an active area (e.g., active area 106 of FIG. 1) of theelectrode substrate. The outer electrode may cover more than 25% of theactive area of the electrode substrate.

At block 525, the process may optionally include electrically connectingthe electrodes with terminals to connect the CRE to an interface, suchas an interface to systems 400 or 450 in FIGS. 4A and 4B. For example,the terminals may be separate leads (e.g., leads 110 of FIG. 1) that canbe plugged into an active device (e.g., controller 402 of FIG. 4A). Invarious embodiments, one or more electrodes may be shorted together,thereby providing a “quasi-CRE” configuration of a lower number ofrecording sites. For example, a tripolar CRE (e.g., CRE 100 of FIG. 1)with the two electrodes shorted together may be referred to as aquasi-bipolar CRE. In some embodiments, the CRE configuration may beoptimized by combining signals from all the recording surfaces into aLaplacian estimate. Such an approach may result in higher Laplacianestimation accuracy and radial attenuation.

B. Process for Determining Functional of Potential

FIG. 6 is a flow chart illustrating an example process 600 fordetermining a functional of an electrostatic potential measurable by aCRE (e.g., CRE 100 of FIG. 1), according to some embodiments. Process600 may be performed in a system such as system 800 of the example ofFIG. 8 or computing device 404 of FIG. 4B, for example, in coordinationwith one or more operations of process 700 of FIG. 7, below.

At block 610, the system may receive information specifying ageometrical configuration of the CRE. In a typical example, this mayinclude a number n of electrodes excluding the central electrode (e.g.,rings) in the CRE and/or the radii and widths of the electrodes. In someembodiments, the inter-electrode spacings may be non-uniform.

At block 620, the system may determine a set of coefficients forLaplacian estimation associated with a series expansion of theelectrostatic potential for the geometrical configuration of the CRE.The system may calculate potentials on all recording surfaces using aseries expansion of the electrostatic potential for the geometricalconfiguration. The potentials may be converted to potential differencesof the form “ring minus disc”, by calculating a difference between thepotential on an electrode (e.g., the middle electrode, the outerelectrode, etc.) and the central electrode. The potential differencesmay be combined into a system of equations, for which the solutions arecoefficients that allow cancellation of truncation terms in the Taylorseries expansion up to the order of 2n, where “n” is the number ofelectrodes excluding the central electrode.

Determining the coefficients for Laplacian estimation may be based on acancellation of at least a first truncation term of the series expansionof the electrostatic potential measured by the CRE. Specifically, thechoice of coefficients may result in the cancellation of the firsttruncation term. In an embodiment, the coefficients are chosen based onthis cancellation. The first truncation term may have an order 2n. In anembodiment, the system may cancel multiple truncation terms. Typically,this may include n−1 truncation terms of even order, up to the order of2n.

The system may determine a set of coefficients including at least afirst and a second coefficient corresponding to respective electrodes ofthe CRE. For example, for a tripolar CRE (e.g., CRE 303 of FIG. 3C), thecoefficients determined may be substantially equal to 952/1227 for thedifference of the inner electrode's potential from the central electrodepotential, and −6/409 for the difference of the outer electrode'spotential from the central electrode potential (equivalent to −53 and −1for a preamplifier configured for integer coefficients). In variousembodiments, the first coefficient is between −60 and −10 times thesecond coefficient, between −70 and −10 times the second coefficient, orbetween −80 and −10 times the second coefficient, or may fall within abroader range less than −10 times the second coefficient. In order touse all the information measured by the electrodes of the TCRE, bothcoefficients may be nonzero.

At block 630, the system may estimate a dependence of the Laplacian on aset of potential differences, including at least a first and a secondpotential difference corresponding to respective electrodes of the CRE.In an embodiment, the system can estimate a dependence of a differentfunctional. In an embodiment, the estimated dependence of the Laplacianmay involve a linear combination of the set of potential differences,wherein a respective potential difference is multiplied by a respectivecoefficient of the set of coefficients.

In some embodiments, the system can further transmit instructions toconfigure an electrophysiological monitoring system based on thedetermined set of coefficients. In an embodiment, the system may includean amplification device configured to combine the potential differencesmeasured by the CRE based on the determined coefficients. For example,the system may use a custom preamplifier board to calculate theLaplacian, and this Laplacian estimate may be sent to the clinicalamplifier for each CRE.

C. Process of Recording Electrophysiological Signals

FIG. 7 is a flow chart illustrating an example process 700 for measuringa response signal by a CRE (e.g., CRE 100 of FIG. 1) using a clinicalsystem (e.g., system 400 of FIG. 4), in accordance with someembodiments. As described in reference to FIG. 4A, a system may beconfigured for electrophysiological measurement of a patient, including,but not limited to seizure monitoring, EEG, ECG, etc. For example,process 700 may optionally include block 705 at which one or more CREsmay be placed at a number of positions on the patient. The placement maybe localized to a specific region of the patient, such as overlying aspecific nerve or organ, or may be distributed in an array on a broadregion, such as the scalp or the abdomen.

At block 710, the system may optionally provide a signal to a CRE or tomultiple CREs arranged in an array. The signal provided to the patientmay be a monitoring signal or a stimulation signal, EEG, brain-computerinterface signals, seizure onset detection, detection of high-frequencyoscillations and seizure onset zones, as well as signals implemented inapplications involving electroenterograms, ECGs, electrohysterograms, orany other kind of electrophysiological monitoring.

At block 715, the system may detect a response signal. Response signalsmay be measured as potentials at one or more electrodes of the CRE, andmay be generated by physiological processes of the patient (e.g.,patient 408 of FIG. 4A). The response signals may be generated inresponse to electrical signals from a controller of the system (e.g.,controller 402 of FIG. 4A). Optionally, at block 720, the responsesignal may be measured at a different electrode than the electrode usedto provide the monitoring or stimulation signal to the patient at block710. For example, in the context of the CRE 100 of FIG. 1, the signalmay be provided to the patient between the outer electrode 104 d and thecentral electrode 104 a, while a second CRE may be positioned near theCRE 100 to record the response signal. In some example, the responsesignal may be measured by one or more of the middle electrodes 104 b-c.Optionally, at block 725 the response signal may be passed by thecontroller 402, which may perform some filtering and/or processing, to acomputing device of the system (e.g., computing device 404 of FIG. 4A).

At block 730, the response signal may optionally be used to estimate aLaplacian. As described in more detail in reference to FIG. 6, a CRE oran array of CREs may measure the surface Laplacian, or the secondspatial derivative, of the electrostatic potential on a surface of thepatient. In some embodiments, the process of estimating the Laplacianmay include applying linear combination coefficients for the potentialsmeasured by the CRE. For example, an amplifier or preamplifier (e.g.,amplifier or preamplifier 464 of FIG. 4B) included in or associated withthe controller may be configured to calculate a Laplacian estimate fromthe potentials measured at block 715, using the coefficients.

V. Additional Considerations

FIG. 8 illustrates examples of components of a computer system 800,according to at least one example. The computer system 800 may be asingle computer such as a user computing device and/or can represent adistributed computing system such as one or more server computingdevices.

The computer system 800 may include at least a processor 802, a memory804, a storage device 806, input/output peripherals (I/O) 808,communication peripherals 810, and an interface bus 812. The interfacebus 812 is configured to communicate, transmit, and transfer data,controls, and commands among the various components of the computersystem 800. The memory 804 and the storage device 806 includecomputer-readable storage media, such as Radom Access Memory (RAM), ReadROM, electrically erasable programmable read-only memory (EEPROM), harddrives, CD-ROMs, optical storage devices, magnetic storage devices,electronic non-volatile computer storage, for example FLASH® memory, andother tangible storage media. Any of such computer-readable storagemedia can be configured to store instructions or program codes embodyingaspects of the disclosure. The memory 804 and the storage device 806also include computer-readable signal media. A computer-readable signalmedium includes a propagated data signal with computer-readable programcode embodied therein. Such a propagated signal takes any of a varietyof forms including, but not limited to, electromagnetic, optical, or anycombination thereof. A computer-readable signal medium includes anycomputer-readable medium that is not a computer-readable storage mediumand that can communicate, propagate, or transport a program for use inconnection with the computer system 800.

Further, the memory 804 includes an operating system, programs, andapplications. The processor 802 is configured to execute the storedinstructions and includes, for example, a logical processing unit, amicroprocessor, a digital signal processor, and other processors. Thememory 804 and/or the processor 802 can be virtualized and can be hostedwithin another computing system of, for example, a cloud network or adata center. The I/O peripherals 808 include user interfaces, such as akeyboard, screen (e.g., a touch screen), microphone, speaker, otherinput/output devices, and computing components, such as graphicalprocessing units, serial ports, parallel ports, universal serial buses,and other input/output peripherals. The I/O peripherals 808 areconnected to the processor 802 through any of the ports coupled to theinterface bus 812. The communication peripherals 810 are configured tofacilitate communication between the computer system 800 and othercomputing devices over a communications network and include, forexample, a network interface controller, modem, wireless and wiredinterface cards, antenna, and other communication peripherals.

In some embodiments, the system and methods described herein candetermine a functional of an electrostatic potential, the electrostaticpotential measurable by CRE comprising at least a middle electrode andan outer electrode, the middle electrode and the outer electrodeconcentric with a central electrode. The system may receive informationspecifying a geometrical configuration of the CRE. The system may thenestimate a dependence of the functional on a set of potentialdifferences comprising at least a first potential differencecorresponding to the middle electrode and a second potential differencecorresponding to the outer electrode, by at least determining a set ofcoefficients for Laplacian estimation associated with a series expansionof the electrostatic potential for the geometrical configuration.Estimating the dependence of the functional on a set of potentialdifferences may further include determining a set of coefficients forthe dependence, the set of coefficients comprising at least a nonzerofirst coefficient of the first potential difference and a nonzero secondcoefficient of the second potential difference, wherein the firstcoefficient is between −60 and −10 times the second coefficient, between−70 and −10 times the second coefficient, between −80 and −10 times thesecond coefficient, or a wider range, for a TCRE.

While the present subject matter has been described in detail withrespect to specific embodiments thereof, it will be appreciated thatthose skilled in the art, upon attaining an understanding of theforegoing may readily produce alterations to, variations of, andequivalents to such embodiments. Accordingly, it should be understoodthat the present disclosure has been presented for purposes of examplerather than limitation, and does not preclude inclusion of suchmodifications, variations, and/or additions to the present subjectmatter as would be readily apparent to one of ordinary skill in the art.Indeed, the methods and systems described herein may be embodied in avariety of other forms; furthermore, various omissions, substitutionsand changes in the form of the methods and systems described herein maybe made without departing from the spirit of the present disclosure. Theaccompanying claims and their equivalents are intended to cover suchforms or modifications as would fall within the scope and spirit of thepresent disclosure.

Unless specifically stated otherwise, it is appreciated that throughoutthis specification discussions utilizing terms such as “processing,”“computing,” “calculating,” “determining,” and “identifying” or the likerefer to actions or processes of a computing device, such as one or morecomputers or a similar electronic computing device or devices, thatmanipulate or transform data represented as physical electronic ormagnetic quantities within memories, registers, or other informationstorage devices, transmission devices, or display devices of thecomputing platform.

The system or systems discussed herein are not limited to any particularhardware architecture or configuration. A computing device can includeany suitable arrangement of components that provide a result conditionedon one or more inputs. Suitable computing devices include multipurposemicroprocessor-based computing systems accessing stored software thatprograms or configures the computing system from a general purposecomputing apparatus to a specialized computing apparatus implementingone or more embodiments of the present subject matter. Any suitableprogramming, scripting, or other type of language or combinations oflanguages may be used to implement the teachings contained herein insoftware to be used in programming or configuring a computing device.

Embodiments of the methods disclosed herein may be performed in theoperation of such computing devices. The order of the blocks presentedin the examples above can be varied—for example, blocks can bere-ordered, combined, and/or broken into sub-blocks. Certain blocks orprocesses can be performed in parallel.

Conditional language used herein, such as, among others, “can,” “could,”“might,” “may,” “e.g.,” and the like, unless specifically statedotherwise, or otherwise understood within the context as used, isgenerally intended to convey that certain examples include, while otherexamples do not include, certain features, elements, and/or steps. Thus,such conditional language is not generally intended to imply thatfeatures, elements and/or steps are in any way required for one or moreexamples or that one or more examples necessarily include logic fordeciding, with or without author input or prompting, whether thesefeatures, elements and/or steps are included or are to be performed inany particular example.

The terms “comprising,” “including,” “having,” and the like aresynonymous and are used inclusively, in an open-ended fashion, and donot exclude additional elements, features, acts, operations, and soforth. Also, the term “or” is used in its inclusive sense (and not inits exclusive sense) so that when used, for example, to connect a listof elements, the term “or” means one, some, or all of the elements inthe list. The use of “adapted to” or “configured to” herein is meant asopen and inclusive language that does not foreclose devices adapted toor configured to perform additional tasks or steps. Additionally, theuse of “based on” is meant to be open and inclusive, in that a process,step, calculation, or other action “based on” one or more recitedconditions or values may, in practice, be based on additional conditionsor values beyond those recited. Similarly, the use of “based at least inpart on” is meant to be open and inclusive, in that a process, step,calculation, or other action “based at least in part on” one or morerecited conditions or values may, in practice, be based on additionalconditions or values beyond those recited. Headings, lists, andnumbering included herein are for ease of explanation only and are notmeant to be limiting.

The various features and processes described above may be usedindependently of one another, or may be combined in various ways. Allpossible combinations and sub-combinations are intended to fall withinthe scope of the present disclosure. In addition, certain method orprocess blocks may be omitted in some implementations. The methods andprocesses described herein are also not limited to any particularsequence, and the blocks or states relating thereto can be performed inother sequences that are appropriate. For example, described blocks orstates may be performed in an order other than that specificallydisclosed, or multiple blocks or states may be combined in a singleblock or state. The example blocks or states may be performed in serial,in parallel, or in some other manner. Blocks or states may be added toor removed from the disclosed examples. Similarly, the example systemsand components described herein may be configured differently thandescribed. For example, elements may be added to, removed from, orrearranged compared to the disclosed examples.

1. (canceled)
 2. A neurophysiological monitoring system comprising: adisplay device; an electrode device comprising a plurality ofelectrodes; a controller connected to the electrode device; and acomputing device connected to the controller and the display device, thecomputing device comprising one or more processors and one or morememories storing instructions that, when executed by the one or moreprocessors, cause the computing device to at least: receive geometricalinformation specifying a geometrical configuration of the electrodedevice, the geometrical configuration defining a quantity of electrodesof the plurality of electrodes and dimensional relationships between aportion of the plurality of electrodes; receive, from the controller, anelectrostatic potential signal corresponding to an electrostaticpotential measured between at least two electrodes of the plurality ofelectrodes; determine, using a finite dimension model and based at leastin part on the geometrical configuration, a set of coefficients of asurface Laplacian estimate associated with the electrostatic potentialsignal; and determine, using the finite dimension model and based atleast upon the set of coefficients and the electrostatic potentialsignal, the surface Laplacian estimate.
 3. The neurophysiologicalmonitoring system of claim 2, wherein the electrode device comprises aconcentric ring electrode having: a central disc electrode having afirst radius “R” relative to a center point of the central discelectrode; a middle ring electrode concentric with the central discelectrode, the middle ring electrode having a first width characterizedby a second radius and a third radius from the center point, the thirdradius greater than the second radius, the first width comprising afirst difference between the third radius and the second radius; and anouter ring electrode concentric with the central disc electrode and themiddle ring electrode, the outer ring electrode having a second widthcharacterized by a fourth radius and a fifth radius from the centerpoint, the fourth radius greater than the third radius and the fifthradius greater than the fourth radius, the second width comprising asecond difference between the fifth radius and the fourth radius.
 4. Theneurophysiological monitoring system of claim 3, wherein the dimensionalrelationships of the geometrical information define the first radius,the first width, and the second width.
 5. The neurophysiologicalmonitoring system of claim 3, wherein receiving the electrostaticpotential signal comprises receiving a first potential signalcorresponding to the central disc electrode, a second potential signalcorresponding to the middle ring electrode, and a third potential signalcorresponding to the outer ring electrode.
 6. The neurophysiologicalmonitoring system of claim 5, wherein determining the surface Laplacianestimate comprises determining a linear combination of the set ofcoefficients with a first potential difference and a second potentialdifference, the first potential difference characterized by the firstpotential signal and the second potential signal, and the secondpotential difference characterized by the first potential signal and thethird potential signal.
 7. The neurophysiological monitoring system ofclaim 2, wherein the set of coefficients improve an accuracy of thesurface Laplacian estimate compared to a second surface Laplacianestimate determined using a negligible dimensions model.
 8. Theneurophysiological monitoring system of claim 2, wherein the electrodedevice is a first electrode device, and the system further comprisesadditional electrode devices configured to be arranged in an array. 9.The neurophysiological monitoring system of claim 2, wherein the one ormore memories store further instructions that cause the computing deviceto further: transmit, to the display device, display informationcorresponding to the surface Laplacian estimate.
 10. Theneurophysiological monitoring system of claim 2, wherein receiving thegeometrical information specifying the geometrical configurationcomprises one of: receiving the geometrical information from thecontroller; receiving the geometrical information from an input deviceof the computing device; or receiving the geometrical information fromthe one or more memories.
 11. A method for electrophysiologicalmonitoring, the method comprising: providing, by a controller of amonitoring system, a signal to at least one electrode of an electrodedevice comprising a plurality of electrodes, each electrode of theplurality of electrodes characterized by at least a dimensional value;detecting, by the controller, a response signal, the response signalgenerated in response to the signal; and determining, using a finitedimension model and based at least on the response signal and thedimensional values of the plurality of electrodes, a surface Laplacianestimate.
 12. The method of claim 11, wherein determining the surfaceLaplacian estimate comprises: determining, by a computing device of themonitoring system, a set of coefficients associated with the responsesignal; providing, to a preamplifier, the set of coefficients; andcalculating, by the preamplifier and based at least in part on the setof coefficients, the surface Laplacian estimate.
 13. The method of claim11, wherein the electrode device is a first electrode device, andwherein detecting the response signal comprises detecting the responsesignal from a second electrode device.
 14. The method of claim 11,wherein providing the signal comprises providing a pulsed electricalstimulation signal to the electrode device.
 15. The method of claim 11,wherein the electrode device is a first electrode device, wherein thefirst electrode device is positioned on a surface of a subject, andwherein additional electrode devices are positioned on the surface ofthe subject in an array with the first electrode device.
 16. The methodof claim 15, wherein the surface comprises a scalp of the subject. 17.One or more computer-readable storage media storing instructions that,when executed by a computer system, cause the computer system to performoperations comprising: receiving information specifying a geometricalconfiguration of an electrode device comprising a plurality ofelectrodes, the geometrical configuration defining a quantity ofelectrodes of the plurality of electrodes and dimensional relationshipsbetween a portion of the plurality of electrodes; receiving, from theelectrode device, an electrostatic potential signal corresponding to anelectrostatic potential measured between at least two electrodes of theplurality of electrodes; determining, using a finite dimension model andbased at least in part on the geometrical configuration, a set ofcoefficients of a surface Laplacian estimate associated with theelectrostatic potential signal; and determining, using the finitedimension model and based at least upon the set of coefficients and theelectrostatic potential signal, the surface Laplacian estimate.
 18. Theone or more computer-readable storage media of claim 17, wherein theelectrode device is a concentric ring electrode device, and wherein thedimensional relationships of the geometrical information define aplurality of widths corresponding to the plurality of electrodes. 19.The one or more computer-readable storage media of claim 17, wherein theelectrode device is a tripolar concentric ring electrode device having acentral disc electrode, a middle ring electrode, and an outer ringelectrode, and wherein receiving the electrostatic potential signalcomprises receiving a first potential signal corresponding to thecentral disc electrode, a second potential signal corresponding to themiddle ring electrode, and a third potential signal corresponding to theouter ring electrode.
 20. The one or more computer-readable storagemedia of claim 17, wherein determining the set of coefficients comprisescomputing the set of coefficients using the finite dimensions model toimprove an accuracy of the surface Laplacian estimate compared to asecond surface Laplacian estimate determined using a negligibledimensions model.
 21. The one or more computer-readable storage media ofclaim 20, wherein the set of coefficients correspond to parameters ofthe finite dimensions model, the set of coefficients determined by theparameters that provide a lowest truncation error of the surfaceLaplacian estimate.